Distinct Fringe Subtrees in Random Trees

05/10/2021
by   Louisa Seelbach Benkner, et al.
0

A fringe subtree of a rooted tree is a subtree induced by one of the vertices and all its descendants. We consider the problem of estimating the number of distinct fringe subtrees in two types of random trees: simply generated trees and families of increasing trees (recursive trees, d-ary increasing trees and generalized plane-oriented recursive trees). We prove that the order of magnitude of the number of distinct fringe subtrees (under rather mild assumptions on what `distinct' means) in random trees with n vertices is n/√(log n) for simply generated trees and n/log n for increasing trees.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

05/26/2020

Compaction for two models of logarithmic-depth trees: Analysis and Experiments

In this paper we are interested in the quantitative analysis of the comp...
03/06/2020

On the Collection of Fringe Subtrees in Random Binary Trees

A fringe subtree of a rooted tree is a subtree consisting of one of the ...
04/19/2018

Entropy rates for Horton self-similar trees

In this paper we examine planted binary plane trees. First, we provide a...
02/07/2020

Recursive PGFs for BSTs and DSTs

We review fundamentals underlying binary search trees and digital search...
08/25/2018

Ranked Schröder Trees

In biology, a phylogenetic tree is a tool to represent the evolutionary ...
10/07/2019

Gröbner bases for staged trees

In this article we consider the problem of finding generators of the tor...
04/12/2019

Dominator Chromatic Numbers of Orientations of Trees

In this paper we prove that the dominator chromatic number of every orie...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.